Turkish Journal of Mathematics
Article Title
The radii of starlikeness and convexity of the functions including derivatives of Bessel functions
DOI
10.55730/1300-0098.3130
Abstract
Let $J_\nu(z)$ denote the Bessel function of the first kind of order $\nu.$ In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function $N_\nu(z)=az^{2}J_{\nu }^{\prime \prime }(z)+bzJ_{\nu }^{\prime }(z)+cJ_{\nu }(z)$ in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag-Leffler expansion for function $N_\nu(z)$ and properties of real and complex zeros of it.
Keywords
Normalized Bessel functions of the fist kind, convex functions, starlike functions, zeros of Bessel function derivatives, radius
First Page
894
Last Page
911
Recommended Citation
KAZIMOĞLU, SERCAN and DENİZ, ERHAN
(2022)
"The radii of starlikeness and convexity of the functions including derivatives of Bessel functions,"
Turkish Journal of Mathematics: Vol. 46:
No.
3, Article 15.
https://doi.org/10.55730/1300-0098.3130
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss3/15
